Plausible competing developmental models show similar or identical structural equation modeling model fit indices, despite making very different causal predictions. One way to help address this problem is incorporating outside information into selecting among models. This study attempted to select among developmental models of children's early mathematical skills by incorporating information about the extent to which models forecast the longitudinal pattern of causal impacts of early math interventions. We tested for the usefulness and validity of the approach by applying it to data from three randomized controlled trials of early math interventions with longitudinal follow-up assessments in the United States (Ns = 1,375, 591, 744; baseline age 4.3, 6.5, 4.4; 17%-69% Black). We found that, across data sets, (a) some models consistently outperformed other models at forecasting later experimental impacts, (b) traditional statistical fit indices were not strongly related to causal fit as indexed by models' accuracy at forecasting later experimental impacts, and (c) models showed consistent patterns of similarity and discrepancy between statistical fit and models' effectiveness at forecasting experimental impacts. We highlight the importance of triangulation and call for more comparisons of experimental and nonexperimental estimates for choosing among developmental models. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

中文翻译：

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结合实验和非实验估计对发育模型进行三角测量。


尽管做出了截然不同的因果预测，但合理的竞争发展模型显示出相似或相同的结构方程建模模型拟合指数。帮助解决此问题的一种方法是将外部信息纳入模型选择中。本研究试图通过纳入有关模型预测早期数学干预因果影响纵向模式程度的信息，在儿童早期数学技能的发展模型中进行选择。我们通过将其应用于美国早期数学干预的三项随机对照试验以及纵向随访评估的数据来测试该方法的有用性和有效性（Ns = 1,375、591、744；基线年龄 4.3、6.5、4.4） ; 17%-69% 黑色）。我们发现，在整个数据集中，（a）一些模型在预测后期实验影响方面始终优于其他模型，（b）传统的统计拟合指数与因果拟合并不密切相关，如模型在预测后期实验影响方面的准确性所索引的那样，并且(c) 模型在统计拟合和模型预测实验影响的有效性之间显示出一致的相似性和差异模式。我们强调三角测量的重要性，并呼吁对实验和非实验估计进行更多比较，以选择发育模型。 （PsycInfo 数据库记录 (c) 2023 APA，保留所有权利）。